I posit that logic is a tool used, sometimes in the thinking process. It has certain rules and can give different conclusions depending upon what assumptions are made. Since not all of us have the same view of reality many start witht different assumptions.

I posit that logic is a tool used, sometimes in the thinking process. It has certain rules and can give different conclusions depending upon what assumptions are made. Since not all of us have the same view of reality many start witht different assumptions.

Precisely. Hence, Euclidean and non-Euclidean Geometry, once it was realized Euclid's Fifth Postulate could not be proven but must in fact remain a postulate.
Not the exact point I wished to make to Mr. Kevvy, but, from another angle, we see how use of logic as a tool in mathematics has then, in turn, led to experiments: what is the curvature of space? (Can Tullio add to this point? I'm not a physicist.)

Thank you Chris, Glenn and betreger for joining in. We can learn from each other.

Isn't that what I just said the conculsion may be sound and logical to them but that doesn't mean there right or Logical even if as you say they have started from a weird point of view to start with , there assumptions ???

Essentially the same. I cannot think of a reason to say otherwise. Except, perhaps, there must be a clear to statement, in a certain form, of an axiom/postulate.

Yes.

For instance the Axiom 1. We take 1 to always be 1. We do not believe 1 to ever be 4. Without this axiom, we can't even define addition.

There are also the axioms of true and false. Without these we can't discuss any logic.

I don't know of any proof of these axioms, nor how anyone could go about proving them as without the proof you don't even have formal logic to build it with. But this result that all we can perceive is based on assumptions should not surprise, or the conclusion that we are unable to even know that we exist.

This bring me to ask which logic is it you wish to discuss. I'm assuming it is not formal logic as that branch of mathematics seems rather well established.

I know this is off topic but you guys looked at Angela's thread how lo can you go man the thread realy cracked me up some of the things she posted secially the 1 about her going near the photocopyer so funny from a guys point of view still laughing

For instance the Axiom 1. We take 1 to always be 1. We do not believe 1 to ever be 4. Without this axiom, we can't even define addition.

This bring me to ask which logic is it you wish to discuss. I'm assuming it is not formal logic as that branch of mathematics seems rather well established.

Obviously (?), I am going to come at this from my own perspective. I'm looking to see what common ground we have amongst those of us here. Is there something I can say to broaden someone else's perspective, or vice versa?

The current impetus is I.D.'s frequent attempts to discuss science in a way that fits his beliefs.
When I originally discussed this, I jumped into Religious Thread 8 back in late 2006. There, as now, I stated I was raised Lutheran but am now agnostic.
My ... ahem ... discussions back then were with Chuck. He claimed to believe nothing. That every correct statement could be proved. He was, of course, coming at it from his brand of an atheist viewpoint.
I believe I.D. now, and Chuck then, from opposite sides, did not have a good understanding of logic, proof and science. Whichever angle we're coming from, if we're going to discuss things (as opposed to bashing each other, which happens often enough), then we could all use a better understanding of logic.
Regarding the first part of your post that I quoted, it remind's me of Chuck's post:

Demonstrate that 2 + 2 = 4.

Peano's Axioms, which I have not done much studying about, worked on putting arithmetic on the same kind of "firm ground" Euclid put geometry on by working out axiomatic reasoning.

Do you want to go into the 2 + 2 = 4 bit? We all know it's true! You can "demonstrate" it to a child by taking two sets of objects with two elements in each set, count up the total and get 4. Is that a proof? Would it surprise you to learn that mathematicians 100-200 years ago felt a need to axiomatize counting and arithmetic, and in fact did so? If you want more details on how they did it, I'll have to get back to you. I've only seen a little bit of it and it is more in the realm of set theory, of which I have only needed to use portions and have not studied as a content area in its own right.

Then again, you should have been more specific. Right now my clock says it is 3:36. 13 hours from now, it will read 4:36. So, 3 + 13 = 4 (modulo 12). Similarly, 2 + 2 = 0 (mod 4). The set of integers {0, 1, ..., n - 1} form a group under addition modulo n. Refer to my previous post about group theory. Again, it has been shown that the set of axioms for group theory are logically consistent, etc. ... . Plus, in some cases, group theory is demonstrably applicable to "real-life" situations, like my clock arithmetic example.

I didn't create this and the people who did had little to no agenda except to abstract upon the familiar in order to expand the body of mathematical knowledge.

So, can 1 ever be 4? Yes, in the sense of "equivalence" modulo 3.

The other portion, which I'll try to respond to tomorrow, was Mr. Kevvy's apparent assertion to I.D. that logic and experimenting are completely separate things. He may have even been asserting logic can be flimsy, using Glenn's looser definition, perhaps?

Sorry sarge my math is only high school and pretty basic but I can I think understand what you said i'm gona have to think about it interesting gona have to read it a few times getting late here and I gotta watch Doctor who's latest episode so till tomorrow bye

Yes a 50yr old waching the Doctor, was brought up on it , I gotta get a life night

As I (and betreger, I take it) see logic as a tool, it stands apart from the math. In my day, in my part of the USA, we were explicitly taught about axiomatic systems/reasoning as part of our 10th grade geometry. How much we understood at the time is another matter.

I would also say that someone may claim to be using logic, but if we come upon two statements from that person (honestly held to be true by that person) that are contradictory, then logical thinking was not used ... or not used extremely well.

There are posts from just a few days ago in a thread that can no longer be seen. That's what got me started on this ... again.

I believe it was Mr. Kevvy, responding to I.D., that said something along the lines of:
"Logic is used by armchair philosophers, and then there are the experimentalists."

Also: "The Earth can't be rotating. Things would fly off. That's not logical."

As for armchair philosophers, there's some truth to this, but anyone that knows enough cannot deny how this has led to applications.

As for the experimentalists, in the time frame that was being referred to, I would guess that the classical age Greeks were just barely moving behind trial and error engineers. Just a bit past those that were able to build pyramids.

Yes, they were developing the scientific method.

But it has taken a long time to work out how we know whether the results of an experiment are significant. It is a marriage of the correct application of logic with the experimentation phase.

An experiment, testing a null versus alternate hypotheses only yields significant evidence against the null hypothesis if the probability (assuming the null hypothesis is true) we would have obtained a sample with such a result is low.

Since probability is relied on, the experimenter is thus bound by the axioms of probability. The statistician, or a user/researcher of probability, is in turn bound by the axioms of calculus because probability draws heavily on calculus.

As I (and betreger, I take it) see logic as a tool, it stands apart from the math. In my day, in my part of the USA, we were explicitly taught about axiomatic systems/reasoning as part of our 10th grade geometry. How much we understood at the time is another matter.

I think we are saying the same thing, math uses logic as a tool but logic is not a subset of math.

As I (and betreger, I take it) see logic as a tool, it stands apart from the math. In my day, in my part of the USA, we were explicitly taught about axiomatic systems/reasoning as part of our 10th grade geometry. How much we understood at the time is another matter.

I think we are saying the same thing, math uses logic as a tool but logic is not a subset of math.

Thanks.
I think, for this to continue, I may have to invite Mr. Kevvy in here. Or, find out who it was that posting what I am responding to (besides I.D.) if it was not Kevvy.

But, since Mr. Kevvy or the poster that talked to I.D. about "armchair philosophers" vs. "experimentalists" has not joined, or no one has responded to the comments in the above link, then this thread has just about run its course. If no one follows up on that post, whether Mr. Kevvy or otherwise, then I may ask the mods to just lock the thread. We're not going anywhere with this right now.